Lecture 3 Problems and Solutions
Q1 - Demand Analysis. The demand for housing is often described as being highly cyclical and very sensitive to housing prices and interest rates. Given these characteristics, describe the effect of each of the following in terms of whether it would increase or decrease the quantity demanded or the demand for housing. Moreover, when price is expressed as a function of quantity, indicate whether the effect of each of the following is an upward or downward movement along a given demand curve or involves an outward or inward shift in the relevant demand curve for housing. Explain your answers.
A. An increase in housing prices
B. A fall in interest rates
C. A rise in interest rates
D. A severe economic recession
E. A robust economic expansion
SOLUTION
A. An increase in housing prices will decrease the quantity demanded and involve an upward movement along the housing demand curve.
B. A fall in interest rates will increase the demand for housing and cause an outward shift of the housing demand curve.
C. A rise in interest rates will decrease the demand for housing and cause an inward shift of the housing demand curve.
D. A severe economic recession (fall in income) will decrease the demand for housing and result in an inward shift of the housing demand curve.
E. A robust economic expansion (rise in income) will increase the demand for housing and result in an outward shift of the housing demand curve.
Q2 - Market Equilibrium. Various beverages are sold by roving vendors at Busch Stadium, home of the St. Louis Cardinals. Demand and supply of the product are both highly sensitive to changes in the weather. During hot summer months, demand for ice-cold beverages grows rapidly. On the other hand, hot dry weather has an adverse effect on supply in that it taxes the stamina of the vendor carrying his or her goods up and down many flights of stairs. The only competition to this service are the beverages that can be purchased at kiosks located throughout the stadium.
Demand and supply functions for ice-cold beverages per game are as follows:
QD = 20,000 - 20,000P + 7,500PK + 0.8Y + 500T / (Demand)QS = 1,000 + 12,000P - 900PL - 1,000PC - 200T / (Supply)
where P is the average price of ice-cold beverage ($ per beverage), PK is the average price of beverages sold at the kiosks ($ per beverage), Y is disposable income per household for baseball fans, T is the average daily high temperature (degrees), PL is the average price of unskilled labor ($ per hour), and PC is the average cost of capital (in percent).
A. / When quantity is expressed as a function of price, what are the ice-cold beverage demand and supply curves if P = $5, PK = $4, Y = $62,500, T = 80 degrees, PL = $10, and PC = 12%.B. / Calculate the surplus or shortage of ice-cold beverage when P = $4, $5, and $6.
C. / Calculate the market equilibrium price-output combination.
ANS:
A. / When quantity is expressed as a function of price, the demand curve for ice-cold beverages per game is:QD = 20,000 - 20,000P + 7,500PK + 0.8Y + 500T
= 20,000 - 20,000P + 7,500(4) + 0.8(62,500) + 500(80)
QD = 140,000 - 20,000P
When quantity is expressed as a function of price, the supply curve for ice-cold beverages per game is:
QS = 1,000 + 12,000P - 900PL - 1,000PC - 200T
= 1,000 + 12,000P - 900(10) - 1,000(12) - 200(80)
QS = -36,000 + 12,000P
B. / The surplus or shortage can be calculated at each price level:
Price
(1) / Quantity
Supplied
(2) / Quantity
Demanded
(3) / Surplus (+) or
Shortage (-)
(4) = (2) - (3)
$4 / QS = -36,000+12,000(4)
= 12,000 / QD = 140,000-20,000(4)
= 60,000 / -48,000
$5 / QS = -36,000+12,000(5)
= 24,000 / QD = 140,000-20,000(5)
= 40,000 / -16,000
$6 / QS = -36,000+12,000(6)
= 36,000 / QD = 140,000-20,000(6)
= 20,000 / +16,000
C. / The equilibrium price is found by setting the quantity demanded equal to the quantity supplied and solving for P:
QD = QS
140,000 - 20,000P = -36,000 + 12,000P
32,000P = 176,000
P = $5.50
To solve for Q, set:
Demand: / QD = 140,000 - 20,000(5.50) = 30,000
Supply: / QS = -36,000 + 12,000(5.50) = 30,000
In equilibrium, QD = QS = 30,000.
Q3 - Cross-Price Elasticity. Surgical Systems, Inc., makes a proprietary line of disposable surgical stapling instruments. The company grew rapidly during the 1990s as surgical stapling procedures continued to gain wider hospital acceptance as an alternative to manual suturing. However, price competition in the medical supplies industry is growing rapidly in the increasingly price-conscious new millennium. During the past year, Surgical Systems sold 6 million units at a price of $14.50, for total revenues of $87 million. During the current year, Surgical Systems' unit sales have fallen from 6 million units to 3.6 million units following a competitor price cut from $13.95 to $10.85 per unit.
A. Calculate the arc cross price elasticity of demand for Surgical Systems' products.
B. Surgical Systems' director of marketing projects that unit sales will recover from 3.6 million units to 4.8 million units if Surgical Systems reduces its own price from $14.50 to $13.50 per unit. Calculate Surgical Systems' implied arc price elasticity of demand.
C. Assuming the same implied arc price elasticity of demand calculated in Part B, determine the further price reduction necessary for Surgical Systems to fully recover lost sales (i.e., regain a volume of 6 million units).
SOLUTION
A. EPX =
=
= 2 (Substitutes)
B. EP =
=
= -4 (Elastic)
C. EP =
-4 =
-4 =
-36P2 + $486 = P2 + $13.50
37P2 = $472.50
P2 = $12.77
This implies a further price reduction of 73 cents because:
ΔP = $12.77 - $13.50 = -$0.73.
Q4 - Income Elasticity. Ironside Industries, Inc., is a leading manufacturer of tufted carpeting under the Ironside brand. Demand for Ironside's products is closely tied to the overall pace of building and remodeling activity and, therefore, is highly sensitive to changes in national income. The carpet manufacturing industry is highly competitive, so Ironside's demand is also very price-sensitive.
During the past year, Ironside sold 30 million square yards (units) of carpeting at an average wholesale price of $15.50 per unit. This year, household income is expected to expected to surge from $55,500 to $58,500 per year in a booming economic recovery.
A. Without any price change, Ironside's marketing director expects current-year sales to soar to 50 million units because of rising income. Calculate the implied income arc elasticity of demand.
B. Given the projected rise in income, the marketing director believes that a volume of 30 million units could be maintained despite an increase in price of $1 per unit. On this basis, calculate the implied arc price elasticity of demand.
C. Holding all else equal, would a further increase in price result in higher or lower total revenue?
SOLUTION
A.
B. Without a price increase, sales this year would total 50 million units. Therefore, it is appropriate to estimate the arc price elasticity from a before-price-increase base of 50 million units:
C. Lower. Since carpet demand is in the elastic range, EP = 8, an increase (decrease) in price will result in lower (higher) total revenues.